Question

please answer 1-3

year	catch	effort
1962	51.8	50.0567
1963	44.3	44.3
1964	48	44.54
1965	44.826	59.9788
1966	39.208	45.3769
1967	48.278	46.6083
1968	37.819	52.2453
1969	31.992	54.1197
1970	29.894	35.6082
1971	39.406	61.2475
1972	34.279	54.7616
1973	27.958	46.5664
1974	36.407	28.5148
1975	27.827	27.1653
1976	33.71	38.8333
1977	32.888	22.0711
1978	35.804	31.362
1979	38.95	25.6873
1980	29.157	19.38
1981	23.748	21.7888
1982	28.333	20.1047
1983	31.945	27.1808
1984	18.434	17.9237
1985	22.531	18.9703
1986	25.587	22.3778
1987	29.777	16.8984
1988	27.906	20.1961
1989	25.757	16.4284
1990	24.503	15.5728
1991	16.608	17.144
1992	18.162	15.7857
1993	18.371	12.1206
1994	16.993	10.3118

ARE 106

Quantitative Methods

Problem Set 3

The data set “BasqueTuna.dat” on Smartsite provides information on the total catch of white tuna in the Basque region of Spain (in tons) and the effort, or total days of fishing (in thousands) to produce this tuna, each year from 1962-1994.

1. Use the data to estimate a simple regression equation of the following form:

catcht  = b0  +b1effortt + et

Report your findings in either table or equation form. Does this regression satisfy CR3? Please show and explain your test for serial correlation at the 95% significance level. Present your results and explain your conclusion

2. Please specify and estimate a better regression model that you can defend, on the basis of economic theory, to explain the production of tuna as a function of effort. Explain why this functional form is better. Present and interpret your results. What is the elasticity of output with respect to effort in this new model?

3. Is serial correlation a problem with the model in (2)?  Please carefully present the results of your test for serial correlation (use the 95% significance level), present your results, and explain your findings.

4. Now re-estimate the model in (2) using the Newey-West method. Report your results and compare them with what you got in (2). What is different, and why?

5. Is there evidence that the marginal product of effort has changed over time?  How? Please show your work, explaining how you test for this and what you find.

6. Does the model in (5) exhibit serial correlation? Please test for this at the 95% level

and present your test results. Is the result different than in (3)? Please speculate on why or why not.

2

Answer 1

The simple linear regression model is

In our case

y= Dependent variable=Catch

x= Independent variable=Effort

Therefore the model is

After fitting the regression model we get,

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	16.8113996	2.478641652	6.782505	1.353E-07	11.7561766	21.86662	11.7561766	21.866623
X Variable 1	0.46712366	0.070758985	6.601616	2.243E-07	0.32280976	0.611438	0.32280976	0.6114376

From the above information we get,

It can be interpreted as follow:

If the effort increase by one unit,the catch is also increase by 0.4671236 unit.